How the design of an experiment influences the nonsensitiveness regions in models with variance components

Nonsensitiveness regions for estimators of linear functions, for confidence ellipsoids, for the level of a test of a linear hypothesis on parameters and for the value of the power function are investigated in a linear model with variance components.The influence of the design of an experiment on the nonsensitiveness regions mentioned is numerically demonstrated and discussed on an example.     

Discrimination distance bounds and statistical applications

Summary Bounds are obtained for the Kullback-Leibler discrimination distance between two random vectorsX andY. IfX is a sequence of independent random variables whose densities have similar tail behavior andY=AX, whereA is an invertible matrix, then the bounds are a product of terms depending onA andX separately. We apply these bounds to obtain the best possible rate of convergence for any estimator of the parameters of an autoregressive process with innovations in the domain of attraction of a stable law. We provide a general theorem establishing the link between total variation proximity of measures and the rate of convergence of statistical estimates to complete the exposition for this application.     

Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

A generalized Stefan problem in several space variables

A multidimensional, multiphase problem of Stefan type, involving quasilinear parabolic equations and nonlinear boundary conditions is considered. Regularization techniques and monotonicity methods are exploited. Existence and uniqueness of a weak solution to the problem, as well as continuous and monotone dependence of the solution upon data are shown.     

Quantification of PCB by dechlorination to biphenyl

Summary Since polychlorinated biphenyls (PCB) are widespread biologically active contaminants in the environment, the need of a sensitive, rapid and simple screening-method for control purposes is obvious. The dechlorination of PCB to biphenyl with LiAlH₄ and subsequent quantification by HPLC and UV detection may fulfil these requirements. Results achieved with this dechlorination method are compared with those obtained by packed-column or capillary-column gas chromatography and EC detection.

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Bestimmung von PCB durch Dechlorierung zu Biphenyl

Zusammenfassung Das ubiquitäre Vorkommen von polychlorierten Biphenylen (PCB) als Kontaminantien in unserer Umwelt erfordert eine empfindliche, rasche und einfache Screening-Methode. Dechlorierung der PCB mit LiAlH₄ zu Biphenyl und anschließende Quantifizierung mittels HPLC und UV-Detektion erfüllt diese Forderungen. Analysenresultate der beschriebenen Dechlorierungsmethode werden verglichen mit Resultaten der Gas-Chromatographie an gepackten Säulen und Capillarsäulen mit EC-Detektion.